All solid materials exhibit viscoelastic behavior. The Maxwell model, which comprises an elastic element (spring) and a viscous element (dashpot) in series, illustrates viscoelasticity: for high frequency vibrations the Maxwell model predicts almost perfect elastic behavior, i.e., minimal energy dissipation, as the motion of the dashpot becomes negligible. For low or moderate frequencies the time scales of the viscoelastic relaxation and vibration are comparable, and they interfere destructively with one another, allowing for more efficient energy dissipation and damping.
The Young's modulus, E, (also known as elastic modulus, modulus of elasticity, or tensile modulus) is a measure of the stiffness of a material. E is the ratio between the tensile stress, σ, divided by the tensile strain, e. E is typically measured on a tensile apparatus which elongates a material and reports the stress needed to produce a certain strain. Alternatively, a sample is compressed and the required stress for a needed deformation is measured. E may be measured under static, or quasi-static, conditions, where the stress does not vary with time. Alternatively, the modulus can be measured under dynamic or time-varying conditions where a material may exhibit properties of elasticity and viscous flow (viscoelasticity) in which case the modulus depends on frequency of deformation and a complex modulus, E*, is defined, where E*=E1+iE2, where E1 is the storage modulus, which is measure of energy stored on a deformation cycle, and E2 is the loss modulus, which is a measure of the energy lost on a cycle.
The shear modulus, G, (also referred to as the modulus of rigidity) of a material, measured under dynamic or time-varying conditions, is the ratio of the shear stress to the shear strain. The shear modulus is typically measured with a parallel-plate rheometer. If the shear rate changes, G depends on the frequency at which the shear changes. Therefore, a complex shear modulus is defined as G*=G1+iG2, where G1 is the storage modulus, which is a measure of energy stored on a deformation cycle, and G2 is the loss modulus, which is a measure of the energy lost on a cycle. For isotropic materials, E=3G for small deformations.
The ratio E1/E2 or G1/G2 is equal to tan(Δ), the ratio of energy lost to energy stored in one cycle. Tan(Δ) is called the loss factor and is a measure of damping efficiency, with greater damping indicated by higher tan(Δ).
Damping or shock-absorbing properties are not determined from static measurements. Damping properties are ascertained by time varying or periodic deformation of the sample. Thus, a soft material (low E) is not necessarily a good candidate for damping. Furthermore, a material that is effective for damping over a certain frequency range may not be effective for damping over another frequency range. Therefore, in reporting a complex modulus (E* or G*), a frequency or frequency range is preferably specified.
Hydrogels comprise water and polymers and are useful for medical and pharmaceutical applications (e.g. see Peppas, N. A.; Editor, Hydrogels in Medicine and Pharmacy, Vol. 3: Properties and Applications. 1987; p 195 pp.). Hydrogels are usually held together via physical or chemical crosslinks, otherwise the polymers of which they are comprised would dissolve in the solvent (water). Polyelectrolyte complexes are interpenetrating complexes of one or more predominantly positive polyelectrolytes and one or more predominantly negative polyelectrolytes. The opposite charges on the polymers form ion pairs between chains, holding the chains together. This ion pairing is a type of physical crosslinking. Polyelectrolyte complexes in contact with aqueous solutions can be considered hydrogels with high crosslinking density.
Recent studies have evaluated the static mechanical properties of polyelectrolyte multilayers, which are ultrathin films of complexed polyelectrolytes. See, for example, Jaber, J. A. and Schlenoff, J. B., J. Am. Chem. Soc. 128, 2940-2947 (2006). Polyelectrolyte multilayers are intermolecular blends of positively and negatively charged polyelectrolyte, wherein each layer of polyelectrolyte added to a growing film has an opportunity to complex efficiently and completely with the existing material, excluding the maximum amount of water. The elastic modulus of these films ranges from kPa to MPa. However, these films are far too thin (a few micrometers or less) to be used for mechanical components in most systems. Furthermore, little is know of the dynamic mechanical properties of molecularly blended complexes of positive and negative polyelectrolytes.
There is a need to prepare articles with dimensions in the millimeter to centimeter to meter scale to provide materials and shapes for biomedical and engineering applications. Polyelectrolyte complexes are prepared in a straightforward manner by mixing solutions of positive and negative polyelectrolytes. However, the resulting precipitate is gelatinous and difficult to process. The dried complexes, for example, are generally infusible and therefore cannot be injection molded or reformed into articles under elevated temperatures. Michaels (U.S. Pat. No. 3,324,068) has disclosed the used of non-volatile plasticizers such as nonvolatile acids, organic oxysulfur compounds and organic oxyphosphorous compounds to decrease the brittleness of polyelectrolyte complexes when they are dried. U.S. Pat. No. 3,546,142 describes a method for creating solutions of polyelectrolyte complexes using aggressive ternary solvents which are mixtures of salt, water and organic solvent. Said solutions of complexes may be reformed into solids by diluting the solution, or by evaporating the solvent (film casting). Mani et al. (U.S. Pat. No. 4,539,373) point out that the solid complexes “are not thermoplastic, i.e. they are not moldable or extrudable, so they must be handled as solutions.” Mani et al. disclose a polyelectrolyte complex comprising thermoplastic repeat units which can be thermally molded.
Polyelectrolyte complexes have been proposed as tissue engineering scaffolding (e.g., see Lim and Sun, Science, 210:908-910 (1980) and Yu et al., U.S. Pat. No. 6,905,875). The purpose of a tissue engineering scaffold is to support and maintain growing cells. Thus, these scaffolds are usually soft and porous and, therefore, not well suited for use as a compressive mechanical support.